Question

if tan x = √ 3 , then find the value of cot x + sin x .​

Answer 1

Given:

• tan x = √ 3

To Find:

• value of cot x + sin x

Solution:

we have,

$\sf \: tan \: x = \sqrt{3} \\ \sf \: but \: tan \: 60 = \sqrt{3} \\ \boxed{ \sf \: x = 60}$

So,

$\sf cot \: x = cot \: 60 = \frac{1}{ \sqrt{3} } \\ \sf sin \:x = sin \: 60 = \frac{ \sqrt{3} }{2}$

now,

$\sf cot \: x + sin \: x = \frac{1}{ \sqrt{3} } + \frac{ \sqrt{3} }{2} \\ \sf = \frac{2 + 3}{2 \sqrt{3} } \\ \sf = \frac{5}{2 \sqrt{3} } \\ = \frac{10 \sqrt{3} }{12} = \frac{5 \sqrt{3} }{6}$

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